Show commands:
SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 139650.jb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.jb1 | 139650ck1 | \([1, 0, 0, -12983188, -31668533758]\) | \(-131661708271504489/159475479581250\) | \(-293158292144601269531250\) | \([]\) | \(23224320\) | \(3.1966\) | \(\Gamma_0(N)\)-optimal |
139650.jb2 | 139650ck2 | \([1, 0, 0, 109559687, 594629247617]\) | \(79116632600119361351/128876220703125000\) | \(-236908726398468017578125000\) | \([]\) | \(69672960\) | \(3.7459\) |
Rank
sage: E.rank()
The elliptic curves in class 139650.jb have rank \(0\).
Complex multiplication
The elliptic curves in class 139650.jb do not have complex multiplication.Modular form 139650.2.a.jb
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.